Properties

Label 369600.b
Number of curves $4$
Conductor $369600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.b1 369600b3 \([0, -1, 0, -19493633, 32986555137]\) \(200005594092187129/1027287538200\) \(4207769756467200000000\) \([2]\) \(28311552\) \(2.9952\)  
369600.b2 369600b2 \([0, -1, 0, -1893633, -119044863]\) \(183337554283129/104587560000\) \(428390645760000000000\) \([2, 2]\) \(14155776\) \(2.6487\)  
369600.b3 369600b1 \([0, -1, 0, -1381633, -623364863]\) \(71210194441849/165580800\) \(678218956800000000\) \([2]\) \(7077888\) \(2.3021\) \(\Gamma_0(N)\)-optimal
369600.b4 369600b4 \([0, -1, 0, 7514367, -956356863]\) \(11456208593737991/6725709375000\) \(-27548505600000000000000\) \([2]\) \(28311552\) \(2.9952\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.b have rank \(1\).

Complex multiplication

The elliptic curves in class 369600.b do not have complex multiplication.

Modular form 369600.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} - 6 q^{13} - 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.